Consider an economy in which people wish to hold money balances worth a total of
5 million goods. They are indifferent between money issued by the central bank and
money issued by private banks (as long as both offer the same rate of return). In the
initial period, the central bank issues $1 million and uses the proceeds to purchase
capital. The central bank owns a stock of capital equal to its stock of money and uses
the return to pay interest on its money. Assume that x = 1.2 and a dollar always buys
two goods. Intermediation, including the payment of interest on money, is costless.
a. What rate of interest ? must the central bank offer to induce people to accepts its
money? Does this satisfy the central bank’s budget constraint?
b. What is the real value of the total amount of money issued by private banks?
c. Is there an equilibrium in which a dollar always purchases three goods? In this
case, what is the real value of money issued by private banks?
d. Argue that the people are indifferent between the equilibrium in which a dollar is
worth three goods and the equilibrium in which a dollar is worth two goods.
e. Suppose the central bank pays no interest on its money but maintains a constant
stock of capital, using the net return from the capital it owns to buy up and burn a
fraction of its money. Find z, the rate of change of the nominal central bank money
stock. Check that the government budget constraint is met. (You should no longer
assume that vt= 2 in all periods.)
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